Specific type of Smoke Simulation
Smoke behavior is heavily impacted by the temperature difference between the smoke and the domain : if the smoke is hotter, it will go up (like smoke from a burning fire) ; if the smoke is colder, it will go down (like mist, or nitrogen).

In the case of a drifting car, the "smoke" is probably more dust than smoke. By the way, it should be the same temperature as the domain (or maybe a little bit colder, to simulate the gravity).

This setting can be found in "Domain/Smoke/Temp. Diff.". I suggest starting with a really low negative value, like -0.0001.